Diffusion kurtosis imaging (DKI) suffers from partial volume effects caused by cerebrospinal fluid (CSF). We propose a DKI+CSF model combined with a framework to robustly estimate the DKI parameters. Since the estimation problem is ill-conditioned, a Bayesian estimation approach with a shrinkage prior is incorporated. Both simulation and real data experiments suggest that the use of this prior leads to a more accurate, precise and robust estimation of the DKI+CSF model parameters. Finally, we show that not correcting for the CSF compartment can lead to severe biases in the parameter estimations.